estweights.RdCreates or adjusts a two-phase survey design object using a logistic regression model for second-phase sampling probability. This function should be particularly useful in reweighting to account for missing data.
estWeights(data,formula,...)
# S3 method for twophase
estWeights(data,formula=NULL, working.model=NULL,...)
# S3 method for data.frame
estWeights(data,formula=NULL, working.model=NULL,
subset=NULL, strata=NULL,...)twophase design object or data frame
Predictors for estimating weights
Model fitted to complete (ie phase 1) data
Subset of data frame with complete data (ie phase 1).
If NULL use all complete cases
Stratification (if any) of phase 2 sampling
for future expansion
If data is a data frame, estWeights first creates a
two-phase design object. The strata argument is used only to
compute finite population corrections, the same variables must be
included in formula to compute stratified sampling probabilities.
With a two-phase design object, estWeights estimates the sampling
probabilities using logistic regression as described by Robins et al
(1994) and adds information to the object to enable correct sandwich
standard errors to be computed.
An alternative to specifying formula is to specify
working.model. The estimating functions from this model will be
used as predictors of the sampling probabilities, which will increase
efficiency to the extent that the working model and the model of
interest estimate the same parameters (Kulich \& Lin 2004).
The effect on a two-phase design object is very similar to
calibrate, and is identical when formula
specifies a saturated model.
A two-phase survey design object.
Breslow NE, Lumley T, Ballantyne CM, Chambless LE, Kulich M. (2009) Using the Whole Cohort in the Analysis of Case-Cohort Data. Am J Epidemiol. 2009 Jun 1;169(11):1398-405.
Robins JM, Rotnitzky A, Zhao LP. (1994) Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89, 846-866.
Kulich M, Lin DY (2004). Improving the Efficiency of Relative-Risk Estimation in Case-Cohort Studies. Journal of the American Statistical Association, Vol. 99, pp.832-844
Lumley T, Shaw PA, Dai JY (2011) "Connections between survey calibration estimators and semiparametric models for incomplete data" International Statistical Review. 79:200-220. (with discussion 79:221-232)
data(airquality)
## ignoring missingness, using model-based standard error
summary(lm(log(Ozone)~Temp+Wind, data=airquality))
#>
#> Call:
#> lm(formula = log(Ozone) ~ Temp + Wind, data = airquality)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -2.34415 -0.25774 0.03003 0.35048 1.18640
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.531932 0.608901 -0.874 0.38419
#> Temp 0.057384 0.006455 8.889 1.13e-14 ***
#> Wind -0.052534 0.017128 -3.067 0.00271 **
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.5644 on 113 degrees of freedom
#> (37 observations deleted due to missingness)
#> Multiple R-squared: 0.5821, Adjusted R-squared: 0.5747
#> F-statistic: 78.71 on 2 and 113 DF, p-value: < 2.2e-16
#>
## Without covariates to predict missingness we get
## same point estimates, but different (sandwich) standard errors
daq<-estWeights(airquality, formula=~1,subset=~I(!is.na(Ozone)))
summary(svyglm(log(Ozone)~Temp+Wind,design=daq))
#>
#> Call:
#> svyglm(formula = log(Ozone) ~ Temp + Wind, design = daq)
#>
#> Survey design:
#> estWeights(airquality, formula = ~1, subset = ~I(!is.na(Ozone)))
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.531932 0.831535 -0.640 0.5237
#> Temp 0.057384 0.008432 6.806 5.07e-10 ***
#> Wind -0.052534 0.020279 -2.591 0.0108 *
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for gaussian family taken to be 0.3130098)
#>
#> Number of Fisher Scoring iterations: 2
#>
## Reweighting based on weather, month
d2aq<-estWeights(airquality, formula=~Temp+Wind+Month,
subset=~I(!is.na(Ozone)))
summary(svyglm(log(Ozone)~Temp+Wind,design=d2aq))
#>
#> Call:
#> svyglm(formula = log(Ozone) ~ Temp + Wind, design = d2aq)
#>
#> Survey design:
#> estWeights(airquality, formula = ~Temp + Wind + Month, subset = ~I(!is.na(Ozone)))
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.577759 0.832906 -0.694 0.4893
#> Temp 0.057689 0.008394 6.872 3.65e-10 ***
#> Wind -0.048750 0.020524 -2.375 0.0192 *
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for gaussian family taken to be 0.323215)
#>
#> Number of Fisher Scoring iterations: 2
#>